cp's OEIS Frontend

A042987 Primes congruent to {2, 3, 5, 7} mod 8.

%I A042987 #25 Jun 26 2022 23:17:02
%S A042987 2,3,5,7,11,13,19,23,29,31,37,43,47,53,59,61,67,71,79,83,101,103,107,
%T A042987 109,127,131,139,149,151,157,163,167,173,179,181,191,197,199,211,223,
%U A042987 227,229,239,251,263,269,271,277,283,293,307,311,317,331,347,349,359,367,373,379
%N A042987 Primes congruent to {2, 3, 5, 7} mod 8.
%C A042987 Equivalently, primes p not congruent to 1 (mod 8).
%C A042987 In 1981 D. Weisser proved that a prime not congruent to 1 (mod 8) and >= 7 is irregular if and only if the rational number Zeta_K(-1) is p-adically integral, that is has a denominator not divisible by p, where K is the maximal real subfield of the cyclotomic field of p-th roots of unity. - From Achava Nakhash posting, see Links.
%H A042987 Ray Chandler, <a href="/A042987/b042987.txt">Table of n, a(n) for n = 1..10000</a> (first 1000 terms from Vincenzo Librandi)
%H A042987 Achava Nakhash, <a href="http://mathforum.org/kb/thread.jspa?forumID=253&amp;threadID=1872454">Irregular Primes and Dedekind Zeta Functions</a>
%t A042987 Select[Prime[Range[100]],MemberQ[{2,3,5,7},Mod[#,8]]&]  (* _Harvey P. Dale_, Mar 24 2011 *)
%o A042987 (Magma) [p: p in PrimesUpTo(1200) | p mod 8 in [2, 3, 5, 7]]; // _Vincenzo Librandi_, Aug 08 2012
%Y A042987 Complement in primes of A007519.
%K A042987 nonn,easy
%O A042987 1,1
%A A042987 _N. J. A. Sloane_